


from __future__ import annotations


def       UpperCAmelCase_					(   UpperCAmelCase__	):
					lowercase_					=      0.00
					lowercase_					=      0
					for resistor in resistors:
										if resistor <= 0:
															lowercase_					=      F'''Resistor at index {index} has a negative or zero value!'''
															raise ValueError(a__	)
										first_sum += 1 / float(a__	)
										index += 1
					return 1 / first_sum


def       UpperCAmelCase_					(   UpperCAmelCase__	):
					lowercase_					=      0.00
					lowercase_					=      0
					for resistor in resistors:
										sum_r += resistor
										if resistor < 0:
															lowercase_					=      F'''Resistor at index {index} has a negative value!'''
															raise ValueError(a__	)
										index += 1
					return sum_r


if __name__ == "__main__":
							import doctest

							doctest.testmod()



from __future__ import annotations


def 				lowerCAmelCase__       (			a__    ,     a__ = None    ,     a__ = None    ,     a__ = False    ,     )      ->tuple[int, float, str]:




  '''simple docstring'''

  _UpperCamelCase           =    cipher_alphabet or [chr(a__ ) for i in range(97    ,     123 )]

  # If the argument is None or the user provided an empty dictionary
  if not frequencies_dict:
    # Frequencies of letters in the english language (how much they show up)
    _UpperCamelCase           =    {
        "a": 0.08497,
        "b": 0.01492,
        "c": 0.02202,
        "d": 0.04253,
        "e": 0.11162,
        "f": 0.02228,
        "g": 0.02015,
        "h": 0.06094,
        "i": 0.07546,
        "j": 0.00153,
        "k": 0.01292,
        "l": 0.04025,
        "m": 0.02406,
        "n": 0.06749,
        "o": 0.07507,
        "p": 0.01929,
        "q": 0.00095,
        "r": 0.07587,
        "s": 0.06327,
        "t": 0.09356,
        "u": 0.02758,
        "v": 0.00978,
        "w": 0.02560,
        "x": 0.00150,
        "y": 0.01994,
        "z": 0.00077,
    }
  else:
    # Custom frequencies dictionary
    _UpperCamelCase           =    frequencies_dict

  if not case_sensitive:
    _UpperCamelCase           =    ciphertext.lower()

  # Chi squared statistic values
  _UpperCamelCase           =    {}

  # cycle through all of the shifts
  for shift in range(len(a__ ) ):
    _UpperCamelCase           =    ""

    # decrypt the message with the shift
    for letter in ciphertext:
      try:
        # Try to index the letter in the alphabet
        _UpperCamelCase           =    (alphabet_letters.index(letter.lower() ) - shift) % len(
            a__ )
        decrypted_with_shift += (
            alphabet_letters[new_key].upper()
            if case_sensitive and letter.isupper()
            else alphabet_letters[new_key]
        )
      except ValueError:
        # Append the character if it isn't in the alphabet
        decrypted_with_shift += letter

    _UpperCamelCase           =    0.0

    # Loop through each letter in the decoded message with the shift
    for letter in decrypted_with_shift:
      if case_sensitive:
        _UpperCamelCase           =    letter.lower()
        if letter in frequencies:
          # Get the amount of times the letter occurs in the message
          _UpperCamelCase           =    decrypted_with_shift.lower().count(a__ )

          # Get the excepcted amount of times the letter should appear based
          # on letter frequencies
          _UpperCamelCase           =    frequencies[letter] * occurrences

          # Complete the chi squared statistic formula
          _UpperCamelCase           =    ((occurrences - expected) ** 2) / expected

          # Add the margin of error to the total chi squared statistic
          chi_squared_statistic += chi_letter_value
      else:
        if letter.lower() in frequencies:
          # Get the amount of times the letter occurs in the message
          _UpperCamelCase           =    decrypted_with_shift.count(a__ )

          # Get the excepcted amount of times the letter should appear based
          # on letter frequencies
          _UpperCamelCase           =    frequencies[letter] * occurrences

          # Complete the chi squared statistic formula
          _UpperCamelCase           =    ((occurrences - expected) ** 2) / expected

          # Add the margin of error to the total chi squared statistic
          chi_squared_statistic += chi_letter_value

        # Add the data to the chi_squared_statistic_values dictionary
    _UpperCamelCase           =    (
        chi_squared_statistic,
        decrypted_with_shift,
    )

  # Get the most likely cipher by finding the cipher with the smallest chi squared
  # statistic
  def chi_squared_statistic_values_sorting_key(a__ ) -> tuple[float, str]:
    return chi_squared_statistic_values[key]

  _UpperCamelCase           =    min(
      a__    ,     key=a__    ,     )

  # Get all the data from the most likely cipher (key, decoded message)
  (
      (
      _UpperCamelCase
  )      ,						(
      _UpperCamelCase
  )      ,						
  )           =    chi_squared_statistic_values[most_likely_cipher]

  # Return the data on the most likely shift
  return (
      most_likely_cipher,
      most_likely_cipher_chi_squared_value,
      decoded_most_likely_cipher,
  )




